Solving a Simple RL Circuit: Find My Fault!

[rbwang1225]

Homework Statement

The Attempt at a Solution

$V-R_1I_1-LdI_L/dt=0, V-R_1I_1-R_2I_2=0, I_1=I_L+I_2$
My result is $I_L=(V/R_1)(1-exp[-tR_1R_2/(R_1+R_2)L])$
Where is my fault?
Any help is appreciated!

 

[wukunlin]

have you learned laplace transforms? it is probably unnecessary in this case but the safest way to do problems like this.

 

[gneill]

This being a first order circuit (only one type of reactive component), you know that the resulting waveforms for all the transient values (currents, voltages) will involve decaying exponential functions with a particular time constant. If you can determine the initial conditions and the final conditions, then the exponential functions will connect the two. Simple! The only really tricky bit is determining the time constant, $\tau$.

The problem statement says that the switch is initially closed (prior to time t = 0). So what is the steady-state current through the inductor, and hence the initial current for time t=0⁺? When the switch is opened, what paths are available for current to flow? So what components determine the time constant? What's the eventual value of the inductor current?